Given: You are an engineer working for a construction firm that plans to build an apartment complex. You have a choice of building some combination of one-, two-, and three-bedroom apartments. A one-bedroom apartment requires 1000 board ft of lumber, 10 cu.yds. of concrete, and 20 rolls of insulation. A two-bedroom apartment requires 1400 board ft of lumber, 12 cu.yds. of concrete, and 24 rolls of insulation. A three- bedroom apartment requires 1600 board ft of lumber, 13 cu.yds. of concrete, and 26 rolls of insulation. A one-bedroom apartment rents for $250 per month, a two-bedroom apartment for $300 per month, and a three-bedroom for $325 per month. Local ordinances require at least one three-bedroom apartment for every three one-and-two bedroom apartments. Your firm has set aside 100,000 board ft of lumber, 1200 cu.yds. of concrete, and 2500 rolls of insulation for this project.

Required: Solve this as a linear programming problem to maximize rental income.

Notes: When you run this problem under LP:

To get an Integer Solution: Run under Gomery Cut Algorithms, not on autoselect, with the following last lines added: BOUNDONSUM = 200 and on the next line: ALLINTEGER.

The BOUNDONSUM variable should be set the the approximate sum of all the answers for your variables. I.E. if you think you will be making 300 one bedroom apartments, 100 two bedroom apartments, and 400 three bedroom apartments (perhaps), try the value of boundonsum = 800, the sum of all your answers X1+X2+X3.

BOUNDONSUM is used to assist the program in making a reasonable guess as to where the answer lies. It is used only to speed up the solution, and is not critical that you get it correct. However, the closer you can get it, the fewer dead ends the computer will go down, and the quicker the program will run. In any case, it is required that you put something in there.

#### Discussion:

Hello,

I had a question about problem 5-5 for the CVEN 422 homework due Tuesday.

When it says “Local ordinances require at least one three-bedroom apartment for every three one-and-two bedroom apartments”, does this mean 3*B3 – B1 – B2 >= 0 or 3*B3 – B1 >=0 and 3*B3 – B2 >=0?

Thanks, Jim

Answer:

Number of 1 BR | Number of 2 BR | Number of 3 BR | Legal? |

10 | 21 | 10 | No |

10 | 20 | 10 | Yes |

10 | 19 | 10 | Yes |

1 | 0 | 1 | Yes |

0 | 4 | 1 | No |

If your equations give these Yes and No results, they are correct.